Nuclear incompressibility: From finite nuclei to nuclear matter

Abstract

The recent increase of experimental data concerning the giant monopole resonance energy E M gives information on the incompressibility modulus of nuclear matter, provided one can extrapolate the incompressibility of a nucleus K A, defined by E M =[ h ̵ 2K A /m〈r 2〉] 1 2 , to the infinite medium. We discuss the theoretical interpretation of the coefficients of an A −1 3 expansion of K A by studying the asymptotic behaviour of two RPA sum rules (corresponding to the scaling and the constrained model), evaluated using self-consistent Thomas-Fermi calculations. We show that the scaling model is the most suitable one as it leads to a rapidly converging A −1 3 expansion of the corresponding incompressibility K A s, whereas this is not the case with the constrained model. Some semi-empirical relations between the coefficients of the expansion of K A s are established, which reduce to one the number of free parameters in a best-fit analysis of the experimental data. This reduction is essential due to the still limited number and accuracy of experimental data. We then show the compatibility of the data given by the various experimental groups with this parametrization and obtain a value of K n.m. = 220 ± 20 MeV, in good agreement with more microscopic analyses.